Differentiated Bertrand competition
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As a solution to the Bertrand paradox in economics, it has been suggested that each firm produces a somewhat differentiated product, and consequently faces a demand curve that is downward-sloping for all levels of the firm's price.
An increase in a competitor's price is represented as an increase (for example, an upward shift) of the firm's demand curve.
As a result, when a competitor raises price, generally a firm can also raise its own price and increase its profits.
Calculating the differentiated Bertrand model
- q1 = firm 1’s demand, *q1≥0
- q2 = firm 2’s demand, *q1≥0
- A1 = Constant in equation for firm 1’s demand
- A2 = Constant in equation for firm 2’s demand
- a1 = slope coefficient for firm 1’s price
- a2 = slope coefficient for firm 2’s price
- p1 = firm 1’s price level pr unit
- p2 = firm 2’s price level pr unit
- b1 = slope coefficient for how much firm 2's price affects firm 1's demand
- b2 = slope coefficient for how much firm 1's price affects firm 2's demand
The above figure presents the best response functions of the firms, which are complements to each other.
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